Gene

Biological network

Quantum mechanics

Function (biology)

Control (management)

Algebraic number

Pure mathematics

Biology

Discrete mathematics

Boolean function

Applied mathematics

Stability (learning theory)

Perturbation (astronomy)

Computer science

Gene regulatory network

Genetics

Physics

Mathematics

Pointwise

Mathematical analysis

Boolean network

Artificial intelligence

Combinatorics

Topology (electrical circuits)

Boolean expression

Control theory (sociology)

Gene expression

Parity function

Machine learning

Nonlinear Analysis Hybrid Systems

In genetic regulatory networks, gene mutations are one of natural phenomena, which attract much attention by biological researchers. In modeling gene networks using switched Boolean networks (SBNs), gene mutations can be described by function perturbations, which is a meaningful issue in analyzing function perturbation of SBNs. This paper studies robust stability of SBNs with function perturbation. With the help of semi-tensor product (STP) of matrices, one equivalent algebraic form of SBNs is established. By constructing two state sets, a criterion for global stability of SBNs under arbitrary switching signals is proposed. In order to relax the conditions of global stability, pointwise stabilizability and consistent stabilizability of SBNs are further considered. Based on state reachable sets, several criteria are established for the proposed kinds of stability. Finally, the obtained results are verified by two examples and lac operon in the Escherichia coli, respectively.

Robust stability of Switched Boolean Networks with function perturbation